Title: Applications of linear ordinary differential equations and dynamic system to economics - an example of Taiwan stock index TAIEX

Authors: Nien-Ping Chen; Meng-Rong Li; Tsung-Jui Chiang-Lin; Young-Shiuan Lee; Daniel Wei-Chung Miao

Addresses: Graduate Institute of Finance, National Taiwan University of Science and Technology, Taipei 106, Taiwan ' Department of Mathematical Sciences, National Chengchi University, Taipei 116, Taiwan ' Graduate Institute of Finance, National Taiwan University of Science and Technology, Taipei 106, Taiwan ' Department of Statistics, National Chengchi University, Taipei 116, Taiwan ' Graduate Institute of Finance, National Taiwan University of Science and Technology, Taipei, 106, Taiwan

Abstract: Mean reversion of stock price is an observed phenomenon in finance. It is similar to the concept of Newton's law of cooling. Three models of ordinary differential equation are derived from the concept and solved by dynamic integration. The models are applied to the daily closing price of Taiwan Stock Exchange Capitalisation Weighted Stock Index. Empirical study shows that the models have good fits and forecasts although errors appear during the dynamic forecasting process. The applicability of the models and future modification are also discussed.

Keywords: Newton's law of cooling; nonlinear dynamic system; ordinary differential equation; stock index closing price; Taiwan Stock Exchange Capitalisation Weighted Stock Index.

DOI: 10.1504/IJDSDE.2017.085824

International Journal of Dynamical Systems and Differential Equations, 2017 Vol.7 No.2, pp.95 - 111

Received: 24 May 2016
Accepted: 02 Sep 2016
Published online: 15 Aug 2017 *

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